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苏·Xu · 2022年10月28日

put call parity

NO.PZ2018062007000082

问题如下:

If an underlying asset’s price is less than a related option’s strike price at expiration, a protective put position on that asset versus a fiduciary call position has a value that is:

选项:

A.

lower.

B.

the same.

C.

higher.

解释:

B is correct. On the one hand, buying a call option on an asset and a risk- free bond with the same maturity is known as a fiduciary call. If an underlying asset’s price is less than a related option’s strike price at expiration,the total value of the fiduciary call is X. On the other hand, holding an underlying asset, ST, and buying a put on that asset is known as a protective put. the total value of the protective put is(X-ST)+ST = X . A protective put and a fiduciary call produce the same result.

中文解析:

在T时刻,标的资产价格ST<执行价格K,在此时call option是没有价值的,为0.(因为T时刻是到期日,call的时间价值为0,而ST

所以此时C+K = 0+K=K;

另外一方面,在T时刻,put option的价值=K-ST(因为此时put的时间价值也为0,intrinsic value=K-ST),所以此时P+ST = K - ST + ST = K;

所以C+K = P + S仍然成立。

不是很懂,解析也没看懂,可否详细讲解一下,谢谢。

1 个答案

Lucky_品职助教 · 2022年10月30日

嗨,从没放弃的小努力你好:


本题考查期权平价公式 C+K=P+S ,无论在什么情况,这个等式都成立,左边叫做fiduciary call,右边叫做protective put。

这道题目中涉及到两个组合,组合一是protective put,组合方式long一份执行价格为X的put option,到期时间为T,再持有一份标的资产,该资产在T时刻的价值为ST,那么根据题目要求,T时刻ST

组合二是fiduciary call,组合方式是long 一份执行价格为X的call option,到期时间为T,再持有一份 面值为X,到期日为T的0息债券,T时刻,call 不行权,组合二的总value为X, 这样两个组合在T时刻的总value是相等的,选择B




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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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